1 April 1994 Fast Zernicke decomposition of images with applications to magnetic resonance imaging
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Abstract
A technique for the fast [O(N)] decomposition of images with respect to Zernicke polynomials is presented. The technique is used to compare images that are equivalent up to a rotation, to correct images misaligned by a rotation, to place symmetric images into a known orientation, and for pattern recognition applications in which rotation-invariant image features are desired. Zernicke polynomials form a class of rotation-invariant polynomials defined on the unit disk |z| ≤ 1. Although the generation of the coefficients of the expansion of an image in terms of these polynomials seems computationally inefficient, we show how the O(N) wavelet transform can be used to replace the Zernicke-image inner products by a component-wise product of the wavelet transforms of the Zernicke polynomials and the wavelet transform of the image. We show how the Zernicke decomposition of an image leads to the correction of rotational misalignment of magnetic resonance images, and how a wide class of centerline-symmetric images (such as magnetic resonance images of the head) can be brought into a uniform alignment using the Zernicke technique.
Ian R. Greenshields, Ian R. Greenshields, } "Fast Zernicke decomposition of images with applications to magnetic resonance imaging," Journal of Electronic Imaging 3(2), (1 April 1994). https://doi.org/10.1117/12.171452 . Submission:
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